What is a precise definition for laminar flow that includes “laminar vortex-shedding”?

I can't find a definition for laminar flow that includes vortex structures.

See paper: Numerical calculation of laminar vortex-shedding flow past cylinders and countless others when googled.

• Usually, in the case of unsteady vortex flow around a cylinder, laminar and turbulent boundary layers are distinguished. Experimentally, these flow regimes are easily distinguishable, and the boundary between them is determined by the critical Reynolds number. Numerical models assume that the flow is laminar if the Reynolds number does not exceed the critical number. – Alex Trounev Feb 12 at 15:59
• @AlexTrounev But what would the difference be between a laminar vortex and a turbulent one? – FemtoComm Feb 12 at 17:06
• In the numerical model there is a big difference between the equations of laminar and turbulent flow. If the vortex flow is laminar, this means that the model used equations describing laminar flow. – Alex Trounev Feb 12 at 17:32
• Thank you Alex! You can post an answer if you feel confident – FemtoComm Feb 12 at 18:32
• Vortex shedding doesn't happen for every laminar flow & is not part of the definition. – D. Halsey Feb 12 at 22:29

I can't find a definition for laminar flow that includes vortex structures.

Vortex structures don't figure directly in the definition of laminar flow, in the sense that we can have laminar flow with or without vortex/eddy structures. Laminar pipe flow doesn't have vortex structures (it has "vorticity" which is different), while vortex shedding at low enough Reynolds number is an example of a laminar flow with vortex structures.

The distinction between laminar and turbulent flows is that in a turbulent flow vortex structures occur in a variety of sizes, from the smallest Kolmogorov scale to the integral scale, and also in a variety of shapes (blobs, sheets, tubes, ribbons). But a laminar flow doesn't have such a multiplicity of scales and structures; vortex blobs being shed behind a cylinder or sphere in laminar flow are approximately all the same size (if the Reynolds number is small enough these blobs don't become turbulent after being shed but simply dissipate away). This is a qualitative idea and making it precise requires use of Fourier transform and velocity correlation functions; see Turbulence by P.A. Davidson.

Also there are no separate equations for laminar and turbulent flows; the same Navier-Stokes equation presumably gives rise to both kinds of flow. However when dealing with turbulent flows we often use the averaged form of Navier-Stokes equation (called Reynolds-averaged Navier-Stokes equation) but the resulting equations are not closed (more unknowns than there are equations); so we must adopt ad-hoc models to obtain closure and there are plenty such models. However Navier-Stokes equation can be solved without averaging, and therefore without requiring ad-hoc models, and these simulations are called Direct Numerical Simluations (they are computationally expensive).

• You did not indicate the difference between the models of laminar and turbulent flows. And this is the question that asked @FemtoComm. – Alex Trounev Feb 14 at 17:17
• @AlexTrounev For both laminar and turbulent flow it's just Navier Stokes equation, no models are actually required. Turbulent flow requires models only if you average it or don't want to resolve all the scales (large eddy simulation for example). I have said as much in the last para. Turbulence models explained in detail can be found in the links provided in the answer and of course on internet. – Deep Feb 15 at 5:16
• Thus, you do not see the difference between the models of laminar and turbulent flows, but thousands of other researchers see this difference. They must indicate which model of turbulence is used, including DNS. They should also indicate which laminar fow model is used, including Navier-Stokes. – Alex Trounev Feb 15 at 13:31
• @AlexTrounev May be you should post an answer explaining the models of laminar and turbulent flow. – Deep Feb 17 at 8:53
• Could one say if the vortex formed flows in layers, the vortex is laminar? Like you said, the eddies may not become turbulent given low enough Reynolds. – FemtoComm Feb 17 at 15:06